Validation tests for semi-parametric models

Abstract

Tests are proposed for validation of the hypothesis that a partial linear regression model adequately describes the structure of a given data set. The test statistics are formulated following the approach of Fourier-type conditional expectations first suggested by Bierens [Consistent model specification tests. J Econometr. 1982;20:105–134]. The proposed procedures are computationally convenient, and under fairly mild conditions lead to consistent tests. Corresponding bootstrap versions are compared with alternative procedures for a wide selection of different estimators of the underlying partial linear model.

Keywords:

• semi-linear model
• goodness-of-fit test
• empirical characteristic function
• bootstrap test

MSC2010 Codes::

• G2G08
• G2G09
• G2G10

Acknowledgements

The collaboration between the two authors was supported by LMS Scheme 4 Grant Ref 4902. Simos Meintanis acknowledges support by Special Account Research Grant 11105 of the Department of Economics, National and Kapodistrian University of Athens.